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1. One required property of an universal hash family is that for any distinct objects x,y, P(h(x) = h(y)) = 1/m. What happens if this requirement was not present?
Give an example of a family of functions H such that for any object x and any bucket i, applying a random function h from H meets the condition that P(h(x) = i) = 1/m,
_but_ applying a random function h from H to two distinct objects x,y will always result in a collision.
Hint: there should be m functions...
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